Comparison Note: Reversible vs Irreversible Processes

Feature	Reversible Isothermal	Irreversible (Const. $P_{ext}$ )	Free Expansion
Work formula	$-nRT\ln(V_2/V_1)$	$-P_{ext}\Delta V$	$0$
Heat $q$	$nRT\ln(V_2/V_1)$	$-P_{ext}\Delta V$ (for isothermal ideal gas)	$0$
$\Delta U$	$0$ (ideal gas, isothermal)	$0$ (ideal gas, isothermal)	$0$ (ideal gas)
$\Delta S_{system}$	$nR\ln(V_2/V_1)$	$nR\ln(V_2/V_1)$	$nR\ln(V_2/V_1)$
$\Delta S_{universe}$	$0$	$> 0$	$> 0$
Work magnitude	Maximum	Intermediate	Zero
Realizability	Theoretical limit	Real processes	Real (into vacuum)
Spontaneous?	Borderline (reversible)	Yes	Yes

Key insight: $\Delta S_{system}$ is the same for all three (state function), but $\Delta S_{universe}$ differentiates reversible from irreversible.